The propagation of electromagnetic waves through the atmosphere is highly dependent on the refractive index of the surrounding medium. That index is subject to random variations, being determined by altitude and meteorological conditions. These conditions tend to give rise to so-called atmospheric conduits into which the electromagnetic waves are channeled but which do not remain fixed for any length of time. In some instances, furthermore, part of the signals sent out by a transmitting antenna arrive at a receiving antenna over several paths, namely as a direct ray and as one or more rays reflected by intervening objects. The sum of the signal components traveling over these diverse paths is degraded by phase and amplitude distortions which can be considered due to alterations of the transfer function of the transmission channel involved. The degradations are intensified with increasing transmission rates and complexity of the adopted modulation technique.
Equalizers designed to minimize these distortions can be subdivided into two major groups respectively operating with intermediate-frequency and baseband compensation.
The techniques of intermediate-frequency equalization are generally simpler, both conceptually and technologically, than those relating to baseband equalization; this particularly applies to high-speed transmission. However, i-f equalization does not always assure good compensation, as where the actual distortions deviate significantly from the expected channel distortions for which the equalizer is designed, where significant differences in delay occur among several paths over which respective signal components are received, or in the case of selective fadings produced when the signal component of highest amplitude is not the one undergoing the least propagation delay.
Baseband-equalization techniques, on the other hand, are not subject to those drawbacks. These techniques do not require any precalculation of the characteristics of a given channel model and operate efficiently under the various conditions referred to above.
The most sophisticated methods of this nature (estimate of maximum likelihood of received sequences, or Kalman filtering) are very complex to implement and have therefore been applied up to now mainly in modems for data transmission over telephone lines.
With high-speed transmission over binary radio links, currently employing rates of 140 to 200 Mbit/sec, technological problems leave only two practical choices for baseband equalization, namely filtering with feedback from a decision stage or correction of the coefficients of a transversal filter preceding that stage.
Filtering with decision feedback involves not only structural complexity but also a possibility of error propagation. Thus, the symbols issuing from the decision stage are used for canceling the intersymbol interference due to so-called postcursors so that, if a decision is wrong, the intersymbol interference is doubled and the probability of error in the ensuing sequence is increased.
For the equalization of transversal filters in radio-link transmission, various systems using analog devices have been described in the literature. See, for example:
An article by S. Takenaka et al titled "A Transversal Fading Equalizer for a 16-QAM Microwave Digital Radio", published June 14-18, 1981, IEEE International Conference on Communications, Denver, Colo., pages 46.2.1-46.2.5;
an article by Y. L. Kuo et al titled "A Baseband Adaptive Equalizer for a 16-State QAM Digital System Over Mastergroup Band Analog Networks", published Nov. 29-Dec. 2, 1982, IEEE Globecom Conference, Miami, Fla., pages F.3.6.1-F.3.6.5;
an article by C. L. Chao et al titled "A Comparative Performance Evaluation of Slope Equalizers and Decision-Directed Weight Control Equalizers", same publication, pages F3.4.1-F3.4.7.
The presence of analog multipliers, which are difficult to adjust and of considerable complexity in the case of high transmission rates, makes these systems expensive and prone to malfunction.
Even upon a changeover from analog to digital devices, the need for such multipliers prevents a significant reduction in complexity and cost with high-speed transmission. The elimination of multipliers, in systems pertaining to phase-shift keying (PSK) and to speech transmission, has been described by us in a paper titled "Multiplication-free Equalizers for Multipath Fading Channels", published June 13-18, 1982, IEEE International Conference on Communications, Philadelphia, Pa., pages 4B.3.1-4B.3.5, and in another paper written jointly with F. Rusina, titled "Multiplication-free Filters for Subband Coding of Speech", published May 10-14, 1982, IEEE International Symposium on Circuits and Systems. Those systems, however, lack the capacity of adapting themselves to time-varying distortions typical of radio channels and are therefore unsuitable for the type of equalizer here considered.